1. Field of the Invention
The present invention relates to a mask data correction apparatus, a Fourier transformation apparatus, an up sampling apparatus, a down sampling apparatus, a method of manufacturing a transfer mask, and a method of manufacturing a device having a pattern structure. In particular, the invention relates to improvements in increasing efficiency while maintaining accuracy.
2. Description of the Background Art
In recent years, the advance of scale down in large scale integrated circuits (LSIs) has been tremendous. This is owing to the development of micro-lithography technology. Especially, light transfer technology has still been in the center of micro-lithography technology because of high throughput by mass exposure, achievement of optical technology continuously developed over 100 years, and the like.
However, now that the fabrication size of micro-patterns is smaller than the wavelength of an exposure light, it is important to establish the limitation of light transfer technology and to overcome the limitation of resolution and depth of focus. In order to perform such analysis, a technique of performing optical image calculation and a technique of correcting distortion generated from the calculated optical image are now arousing interest. FIG. 32 is a flow chart illustrating, as one particular example, a procedure of a mask data correction method which was invented by the present inventor and disclosed in Japanese Patent Application Laid-Open No. 8-297692 (1996) (hereinafter referred to as xe2x80x9cliterature Ixe2x80x9d).
This method is fully described in literature I and is known in the art, and it will be thus discussed briefly hereinbelow. When process S90 of this method is started, a circuit design and a layout design are performed (S91, S92), and initially a layout data is stored in a record medium (S93). The layout data defines the shape and hierarchical structure of base elements of a graphic having a hierarchical structure. The layout data is then expanded (S94), and a process condition is inputted (S95). Thereafter, meshes are formed (S96) and an image calculation is performed (S97). In comparison of the result of the image calculation with the layout data, a graphic correction is made (S98), and a correction data as being the result is outputted (S99), thereby completing process S90.
When using these techniques, attentions should be given also to degradation of an optical image that is caused by aberration of an optical system. These techniques are fully described in Japanese Patent Application Laid-Open No. 9-167731 (1997) (hereinafter referred to as xe2x80x9cliterature IIxe2x80x9d) or No. 10-335224 (1998) (hereinafter referred to as xe2x80x9cliterature IIxe2x80x9d), which were invented by the present inventor. In some cases, a long range correlation of full shot level may cause a problem.
In order to perform such evaluation or optimization, it is necessary to check the consistency between the result of calculation and the result of experiment about optical images with regard to various cases. However, the optical image calculation usually requires a large quantity of calculation because, for example, it is required that a mask graphic is subjected to Fourier transformation, followed by inverse Fourier transformation. Thus, numerous proposals for performing Fourier transformation at high speed has been presented. The following methods are generally known.
(1) FFT (Fast Fourier Transformation) which is disclosed in, e.g., xe2x80x9cWaveform Data Processing for Scientific Instrumentationxe2x80x9d by Shigeo Minami, CQ publishing company;
(2) OCA (Optical Coherent Approximation) which is disclosed in, e.g., Y. C Pali and T. Kailath J. OP Soc. Am A, Vol. 11(1994)2438;
(3) Irregular intervals Fourier transformation which is disclosed in, e.g., E. Barouch, B. Bradie, U. Hollerbach, and S. A. Orszag, J. Vac. Sci. and Technol. B8(1990)1432; E. Barouch, B. Bradie, U. Hollerbach, and S. A. Orszag, Proc. SPIE Vol. 1465(1991)254; and E. Barouch, U. Hollerbach, S. A. Orszag, B. Bradie and M. Peckcrar, IEEE Electron Device Lett., EDL-12(1991)513;
(4) Partial coherent approximation which is disclosed in, e.g., M. Yeung: Proc, Kodak Microelectronics Seminar INTERFACE ""85 (KTI Chemicals, Inc, San Diego, 1986) p.115; and M. Yeung: Proc. SPIE Vol. 922(1988)149; and
(5) Massively parallel operation which is disclosed in, e.g., K. Kamon, W. Wakamiya, H. Nagata, K. Moriizumi, T. Miyamoito, Y. Myoi and M. Tanaka; Proc, SPIE Vol. 2512(1995)491; T. Hanawa, K. Kamon, A. Nakae, S. Nakao and K. Moriizumi: Proc, SPIE Vol. 2726(1996)640; and A. Nakae, K. Kamon, T. Hanawa, K. Moriizumi and S. Nakao: Jpn. J. Appl. Phys. Vol.35(1996)6395.
Through these techniques, remarkable high speed has recently been obtained. These techniques, each being extremely effective, have contributed markedly to the innovation of micro-lithography technology. However, a full shot calculation of LSIs cannot be performed satisfactorily even in combination of these, for reasons which are discussed hereinbelow. For instance, in the case of a DRAM of 1G (giga) bit that is under development, a vast number of transistors of 1G are closely disposed longitudinally and transversely to form a memory array. Further, even a logic device has such a configuration that a lot of small-size RAMs are contained. Furthermore, it is assumed that LSIs will be further subjected to high integration in the future.
Conventionally, such a method that a graphic data is processed after a temporal flat expansion (e.g., xe2x80x9cdraculaxe2x80x9d by Cadence Corp.) has usually employed. Whereas in order to handle a large number of graphics, there has recently been developed an apparatus in which operations such as layout verification are performed by utilizing the hierarchical structure of a graphic data (e.g., xe2x80x9cherculesxe2x80x9d by Arant Corp.; xe2x80x9ccaliberxe2x80x9d by Menter Corp.; and xe2x80x9ccloverxe2x80x9d by Lucent Corp.). In these apparatuses, as shown in FIG. 33, high speed processing has been attained by collecting some data at cells 91, and performing a graphic operation while maintaining the relative disposition of cells and the hierarchical structure. In FIG. 33, a plurality of cells 91 are disposed in an image forming region 90, and a graphic base element 92 is disposed in the cells 91.
Since these apparatuses can perform simple operation and comparison between graphics at high speed, they are suitable for use in design rule check, logic operation between simple graphics, or sizing.
However, when a certain graphic influence or correlation is exerted widely over a plurality of cells, it is required to expand each element cell. Thus, it is known not only that high speed data processing cannot be attained but also that processing capacity is lowered in some cases.
In application to optical image calculation, a certain graphic influence extends within the coherence length of an optical system. In some cases, micro loading effect in dry etching or proximity effect in mask drawing extends to about 10 xcexcm. It is therefore necessary to calculate the state that graphic elements interfere or influence with each other. It can be said that such correlation state calculation is rather essential in a variety of process simulations including lithography. Since the above-mentioned optical coherency or various proximity effects usually extend over a plurality of cells, it has conventionally been necessary to expand all the cells for evaluation. As a result, even if the hierarchical data is used in proximity correction calculation, it is finally required to expand all the cells. This makes it impossible to sufficiently exhibit the effectiveness of hierarchical processing.
It is an object of the present invention to overcome the disadvantages in the prior art by providing a mask data correction apparatus, a Fourier transformation apparatus, an up sampling apparatus, a down sampling apparatus, a method of manufacturing a transfer mask, and a method of manufacturing a device having a pattern structure, each of which is capable of increasing processing efficiency while maintaining high accuracy, by the effective use of the hierarchical structure of a layout data.
According to a first aspect of the invention, a mask data correction apparatus in which based on a layout data defining the shape of base elements of a graphic having a hierarchical structure and the hierarchical structure and on a manufacturing process condition, a mask data expressing the pattern form of a transfer mask used in the manufacturing process is created in such a manner as to suppress a distortion expected in the manufacturing process, comprises: a Fourier transformation part to obtain Fourier images of the base elements by performing Fourier transformation of the base elements; a synthesizing part to obtain Fourier image of the graphic by synthesizing the Fourier images of the base elements in Fourier space, based on the hierarchical structure; a spatial filter part subjecting the Fourier image of the graphic to spatial filter processing corresponding to the distortion; an inverse Fourier transformation part subjecting the Fourier image after the spatial filter processing to inverse Fourier transformation, thereby to obtain the inverse Fourier image reflecting the distortion; a graphic transformation part to transform the inverse Fourier image into a graphic; and a graphic correction part to correct the graphic defined by the layout data in such a direction as to suppress the distortion by comparing the graphic outputted from the graphic transformation part with the graphic defined by the layout data, and to output the result as the mask data.
According to a second aspect of the invention, the mask data correction apparatus of the first aspect is characterized in that the distortion includes a drawing distortion caused when the transfer mask is formed by electron beam drawing based on the mask data.
According to a third aspect of the invention, the mask data correction apparatus of the first or second aspect is characterized in that the distortion includes a transfer distortion caused in a transfer image when transfer is performed by using the transfer mask formed based on the mask data.
According to a fourth aspect of the invention, the mask data correction apparatus of the first, second or third aspect is characterized in that the distortion includes an etching distortion caused in an etching pattern when selective etching is performed by using a resist pattern formed by transferring the transfer mask formed based on the mask data.
According to a fifth aspect of the invention, the mask data correction apparatus of one of the first to fourth aspects is characterized in that the distortion includes a polishing distortion caused in a polished pattern when polishing processing of a deposited film is performed after selective etching is performed with a resist pattern formed by transferring the transfer mask formed based on the mask data.
According to a sixth aspect of the invention, the mask data correction apparatus of one of the first to fourth aspects is characterized in that the distortion includes an etch back distortion caused in the pattern subjected to etch back when etch back processing of a deposited film is performed after selective etching is performed with a resist pattern formed by transferring the transfer mask formed based on the mask data.
According to a seventh aspect of the invention, the mask data correction apparatus of one of the first to sixth aspects is characterized in that the Fourier transformation part comprises: a graphic dividing part dividing the base element into a group of element graphics in the form of a triangle, tetragon or circle; and an element graphic Fourier transformation part to perform Fourier transformation per element graphic of the group of element graphics, thereby to obtain their respective Fourier images.
According to an eighth aspect of the invention, the mask data correction apparatus of the seventh aspect is characterized in that the element graphic Fourier transformation part performs integral calculation analytically by using a primitive function, when calculation of spatial frequency components is made to obtain the Fourier image.
According to a ninth aspect of the invention, the mask data correction apparatus of one of the first to eighth aspects further comprises a mesh forming part to set an image forming region in real space and the Fourier space and to set meshes in the image forming region, the mesh forming part comprising: a minimum correlation distance calculating part to calculate a minimum correlation distance in the manufacturing process, based on the manufacturing process condition; and a mesh number optimizing part to determine the number of meshes along two directions crossing in the image forming region such that the mesh width is the largest in the range not exceeding the minimum correlation distance and the number of meshes is a positive integer.
According to a tenth aspect of the invention, the mask data correction apparatus of the ninth aspect is characterized in that the mesh number optimizing part limits the positive integer to a positive integer n that is defined by n=2i3j5k (i, j and k are each zero or a positive integer), and the Fourier transformation part performs the Fourier transformation by using fast Fourier transformation.
According to an eleventh aspect, the mask data correction apparatus according to one of the first to eighth aspects further comprises: a mesh forming part to set an image forming region in real space and the Fourier space and to set meshes in the image forming region; a mesh adding part to add a new mesh into the image data obtained after the spatial filter processing; and a new mesh data setting part to set the value of zero to the image data on the added mesh and then to output the result together with the image data before the mesh is added, and wherein the inverse Fourier transformation part performs the inverse Fourier transformation of the image data outputted from the new mesh data setting part.
According to a twelfth aspect of the invention, the mask data correction apparatus of one of the first to eighth aspects further comprises: a mesh forming part to set an image forming region in real space and the Fourier space and to set meshes in the image forming region; and a mesh removing part to remove some of meshes from the image data obtained after the spatial filter processing, and wherein the inverse Fourier transformation part performs the inverse Fourier transformation of the image data outputted from the mesh removing part.
According to a thirteenth aspect, a method of manufacturing a transfer mask comprises the steps of: (a) creating a mask data by using the mask data correction apparatus according to one of the first to twelfth aspects; and (b) forming a transfer mask by using the mask data created in the step (a).
According to a fourteenth aspect, a method of manufacturing a device having a pattern structure comprises the steps of: (a) creating a mask data by using the mask data correction apparatus according to one of the first to twelfth aspects; (b) forming a transfer mask by using the mask data created in the step (a); (c) forming a resist on the surface of a material of a device to be manufactured; (d) transferring the transfer mask formed in the step (b) to the resist; (e) patterning the resist in the pattern form transferred in the step (d); and (f) performing selective processing of the material by using the patterned resist as a shield.
According to a fifteenth aspect, a Fourier transformation apparatus subjecting a graphic having a hierarchical structure to Fourier transformation, comprises: a graphic dividing part to divide a base element of the hierarchical structure into a group of element graphics in the form of a triangle, tetragon or circle; an element graphic Fourier transformation part in which Fourier transformation is performed per element graphic of the group of element graphics, thereby to obtain their respective Fourier images; and a synthesizing part to obtain Fourier image of the graphic by synthesizing the Fourier image of the base element in Fourier space, based on the hierarchical structure.
According to a sixteenth aspect, an up sampling apparatus subjecting a discrete data to up sampling, comprises: a Fourier transformation part to transform the discrete data into a set of frequency components, by performing Fourier transformation of the discrete data defined in one or more dimensional space; a mesh adding part to make the set of frequency components into data on meshes set in Fourier space of the same dimension as the above-mentioned one or more dimension, and to add a new mesh into the Fourier space; a new mesh data setting part to set the value of zero to the data on the added mesh and to output the result together with the data on the meshes before addition; and an inverse Fourier transformation part performing inverse Fourier transformation of data outputted from the new mesh data setting part.
According to a seventeenth aspect, a down sampling apparatus subjecting a discrete data to down sampling, comprises: a Fourier transformation part to transform the discrete data into a set of frequency components, by performing Fourier transformation of the discrete data defined in one or more dimensional space; a mesh removing part to make the set of frequency components into data on meshes set in Fourier space of the same dimension as the above-mentioned one or more dimension, and to output the result after removing a part of the meshes in the Fourier space; and an inverse Fourier transformation part performing inverse Fourier transformation of data outputted from the mesh removing part.
In the apparatus of the first aspect of the invention, the Fourier image of the entire graphic can be obtained by synthesizing the Fourier images of base elements, based on the hierarchical structure. Thereby, a mask data in which a large number of base elements are contained in a graphic can be corrected at high efficiency while maintaining accuracy.
In the apparatus of the second aspect of the invention, correction is made so as to suppress a distortion including a drawing distortion, thereby to obtain a mask data capable of suppressing the drawing distortion that appears on the transfer mask.
In the apparatus of the third aspect of the invention, correction is made so as to suppress a distortion including a transfer distortion, thereby to obtain a mask data capable of suppressing the transfer distortion that appears on the transfer image.
In the apparatus of the fourth aspect of the invention, correction is made so as to suppress a distortion including an etching distortion, thereby to obtain a mask data capable of suppressing the etching distortion that appears on the etching pattern.
In the apparatus of the fifth aspect of the invention, correction is made so as to suppress a distortion including a polishing distortion, thereby to obtain a mask data capable of suppressing the polishing distortion that appears on the polished pattern.
In the apparatus of the sixth aspect of the invention, correction is made so as to suppress a distortion including an etch back distortion, thereby to obtain a mask data capable of suppressing the etch back distortion that appears on the pattern after etch back.
In the apparatus of the seventh aspect of the invention, the Fourier image of the entire graphic is obtained by dividing the base element into the group of element graphics, each being in the form of a triangle, tetragon or circle; performing Fourier transformation per element graphic; and superimposing the results thus obtained. Therefore, even if the base element has any complicated shape, Fourier transformation to the entire graphic can be achieved in short time without degradation of accuracy. As a result, the mask data can be corrected at higher efficiency without degradation of accuracy.
In the apparatus of the eighth aspect of the invention, by utilizing the fact that a base element is divided into a group of element graphics of simple shape, when calculating spatial frequency components, definite integral calculation is performed analytically by using a primitive function. Thereby, the accuracy of Fourier transformation is further improved while the time required for calculation is further reduced.
In the apparatus of the ninth aspect, the number of meshes is optimized. Therefore, the mask data correction is attainable at high accuracy without requiring the wasteful calculation time.
In the apparatus of the tenth aspect of the invention, the number of meshes is limited to an adequate number for fast Fourier transformation and Fourier transformation is performed by employing fast Fourier transformation. Thereby, the efficiency of calculation is increased without degradation of accuracy.
In the apparatus of the eleventh aspect of the invention, interpolation reflecting the entire graphic is performed because up sampling is carried out in Fourier space. Therefore, there is provided the corrected mask data which is smooth and natural and is unavailable merely by linear interpolation or the like.
In the apparatus of the twelfth aspect of the invention, interpolation that reflects the entire graphic is performed because down sampling is carried out in Fourier space. Therefore, although the number of meshes is reduced, there is provided the corrected mask data which is smooth and natural and is unavailable merely by linear interpolation or the like.
In the method of the thirteenth aspect of the invention, a mask data is created by using the mask data correction apparatus of the present invention, and a transfer mask is formed by using the mask data. Thereby, a transfer mask of high accuracy can be obtained at high efficiency.
In the method of the fourteenth aspect of the invention, a mask data is created by using the mask data correction apparatus of the present invention, and a transfer mask is formed by using the mask data, and further, the transfer mask is used when performing transfer to a resist, patterning of the resist, and selective processing. Thereby, a device having a pattern structure of high accuracy can be obtained at high efficiency.
In the apparatus of the fifteenth aspect of the invention, the Fourier image of the entire graphic is obtained by dividing a base element into a group of elements graphics, each being in the form of a triangle, tetragon or circle; performing Fourier transformation per element graphic; and superimposing the results thus obtained. Therefore, even if the base element has any complicated shape, Fourier transformation to the entire graphic can be achieved in short time without degradation of accuracy.
In the apparatus of the sixteenth aspect of the invention, interpolation reflecting the entire graphic is performed because up sampling is carried out in Fourier space. Therefore, there is provided the data after up sampling which is smooth and natural and is unavailable merely by linear interpolation or the like.
In the apparatus of the seventeenth aspect of the invention, interpolation reflecting the entire graphic is performed because down sampling is carried out in Fourier space. Therefore, although the number of meshes is reduced, there is provided the data after down sampling which is smooth and natural and is unavailable merely by linear interpolation or the like.
These and other objects, features, aspects and advantages of the present invention will become more apparent from the following detailed description of the present invention when taken in conjunction with the accompanying drawings.